Conjectures are statements that use an if, then structure and are commonly presented throughout Geometry (for example, if a triangle has two congruent base angles, then that triangle is isosceles). The math converse of a statement switches the if and then, resulting in a statement that may or may not be true; verifying the truth value of a converse is a common exercise in Geometry.

The converse is when you switch the ifand then of a conditional statement.Well, conditional statement means if somethinghappens then something else mustbe true.But you could think of it asa hypothesis and conclusion.So a converse is not always true.

So let's look at two examples.Here we're being asked find the converseof the statement, then ask yourselfis it true.So this first statement says if itis Monday, then it is a weekday.Well, that's true.If today's Monday then it's a weekday.So the converse is going to take theif and the then and switch them.

Or another way of thinking about it iswe're going to take what comes afterthen and write it after if.So I'm going to say if it is a weekday --so I'm going to take that second partwhich was our conclusion, if it isa weekday, now I need to switch itagain. Then I'm going to say the first part ofmy statement here, which says it is Monday.

So the converse, again, takes a hypothesisin the conclusion and switches them.Well, if it's a weekday, thenMonday is not always true.What if today was Tuesday.Tuesday is a weekday.So not every weekday is Monday.So the statement here is not true.The converse is not true.

Let's look at one more andapply it to geometry.If an angle measures 88 degrees,then it is acute.That's true by definition an acute angleis any angle that measures lessthan 90 degrees but morethan 0 degrees.

So let's find our converse.So I'm going to take the if, and instead ofsaying if an angle measures 88 degrees,I'm going to take the secondpart of this statement.So I'm going to write that instead ofsaying if it's acute, doesn't tell meanything, if an angle is acute, okay.So there I had to add in a couple ofwords to make sure it made sense.Then now I'm going to say the second part.The angle measures 88 degrees.Then the angle measures 88 degrees.

So if we look at this statement, let's sayI had an angle right here that measured75 degrees.Well, it's an acute angle, but it'snot equal to exactly 88 degrees.So the converse of this statement is nottrue as well but not every statementin geometry whose converseis going to be false.So that's not always going to happen.

I just gave two examples here where if youtake the if and the then statement,switch them and evaluate them, you canfind counter examples which makesthe converse not true.